Linear Speedup of Winograd's Matrix Multiplication Algorithm Using an Array Processor

Abstract

Winogradi’s matrix multiplication algorithm halves the number of multiplication operations required of the conventional 0 ( N 3 ) matrix multiplication algoirithm by slightly increasing the number of addition operations. Such it technique can be computatiorially advantageous when the machine performing the matrix computation takes much more time for multiplication over addition operations. This is overwhelmingly the case in the massively parallel computing paradigm, where each processor is extremely simple by itself and the computing power is obtained by the use of a large number of such processors. In this paper, we describe a parallel version of Winograd’s imatrix multiplication algorithm using an array processor and show how to achieve nearly linear speedup over its sequential counterpart.